Given:
The two functions are:
[tex]f(x)=2x^2+1[/tex]
[tex]g(x)=3x-6[/tex]
To find:
The correct statement about the function [tex]f+g[/tex].
Solution:
We have,
[tex]f(x)=2x^2+1[/tex]
[tex]g(x)=3x-6[/tex]
Adding both functions, we get
[tex]f+g=f(x)+g(x)[/tex]
[tex]f+g=2x^2+1+3x-6[/tex]
[tex]f+g=2x^2+3x-5[/tex]
It is a quadratic function. So, option A is incorrect and option B is correct.
The domain of [tex]f+g[/tex] is all real numbers because it is defined for all real values of x. So, option C is incorrect.
The range of [tex]f+g[/tex] cannot be the all real numbers because it has a minimum value of y as the leading coefficient is positive. So, option D is incorrect.
Therefore, the correct option is B.
5.
The cube root for three hundred and forty three is
Punca kuasa tiga bagi tiga ratus empat puluh tiga adalah
A. 343
B. 73
C. 3433
D. 7
D. 7
Hope this helps! :)
______________
Answer:
The cube root of 343 is 7.
Over which interval does f have an average rate of change zero?
A. -3≤x≤5
B. -5≤x≤3
C. 2≤x≤4
D. -3≤x≤-1
Answer:
Step-by-step explanation:
The average rate of change is the slope. Slope has a formula that is the change in y over the change in x, which is a fraction. The only time a fraction can have a vlue of 0 is where the numerator of the fraction is equal to 0 (since we are not allowed to have a denominator of 0). If the change in y is in the top of the slope fraction, then we have to find the interval where the y values are the same. I'll show you one where the y values are not the same so you can compare it to the slope where the y values are the same. We will find the slope of choice A.
When x = -3, y = 0 so the coordinate is (-3, 0).
When x = 5, y = 5 so the coordinate is (5,4). Now let's find the slope (aka average rate of change) between those 2 coordinates:
[tex]m=\frac{4-0}{5-(-3)}=\frac{4}{8}=\frac{1}{2}[/tex] and the top of the fraction is a 1, not a 0, so the average rate of change between these 2 points is 1/2, not 0. Now let's do D.
When x = -3, y = 0 so the coordinate is (-3, 0).
When x = -1, y = 0 so the coordinate is (-1, 0). The slope between these 2 points is
[tex]m=\frac{0-0}{-1-(-3)}=\frac{0}{2}=0[/tex] This fraction is equal to 0 because the numerator is 0. Choice D is the one you want.
verify that :- 5/8x(7/9-11/6)=(5/8x7/9)-(5/8x11/6)
please answer
The sides of a number cube are labeled 1 through 6.
Suppose you toss the cube 600 times. About how many times
would you expect the cube to land on 1?
Answer:
100 times for 1
Step-by-step explanation:
If the cube is a fair one, you would expect it to land on each number about 1/6 of the time. Since 1 is one of the faces, you would expect to land on it 1/6 of the time.
(1/6)*600=100
So any number should land 100 times
b) 6 x (5 + 4) 1) 32 - (14 - 6) X 3 35 - {15 - (19 + 5)=3} 1) 5 {13 + 12 + 3 (2 x 2)
Answer:
your answer is 1275
Step-by-step explanation:
ccifufbfjrorwfeejeidiffgfkxxocyegdo
A rectangular vegetable farm measures 45 m by 15 m. It has also a path of 1m wide. What is the area of the path?
[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
[tex]\huge\underline{\sf{\red{Problem:}}}[/tex]
A rectangular vegetable farm measures 45 m by 15 m. It has also a path of 1m wide. What is the area of the path?[tex]\underline{\sf{\red{Formula\:for\: area\: of \:rectangular\: form:}}}[/tex]
[tex]\quad\quad\quad\quad\boxed{\sf{\red{➢} \: \sf{a=l×b}} }[/tex]
[tex]\underline{\sf{\red{Given:}}}[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{Length\:of\:rectangular\:form = 45m} }[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{Breadth\:of\:rectangular\:form = 15m} }[/tex]
[tex]\underline{\sf{\red{Solution:}}}[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{a=l×b} }[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{a=45m×15m} }[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{a=\boxed{\sf{{675m}^{2}}}} }[/tex]
[tex]\underline{\sf{\red{For\:rectangular\: form\:with\:path:}}}[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{Length\:of\:rectangular\:form = 45m+2=47m} }[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{Breadth\:of\:rectangular\:form = 15m+2=17m} }[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{a=l×b} }[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{a=47m×17m} }[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{a=\boxed{\sf{{799m}^{2}}}} }[/tex]
[tex]\huge\underline{\sf{\red{Area\:of\:path:}}}[/tex]
[tex]\quad\quad\quad\quad\sf{\red{➢} \: \sf{a={799m}^{2}-{675m}^{2}} }[/tex]
[tex]\quad\quad\quad\quad\boxed{\sf{\red{➢} \: \sf{a={124m}^{2}} }}[/tex]
[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]
[tex]\huge\quad\quad\underline{\boxed{\sf{\red{a={124m}^{2}} }}}[/tex]
[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
[tex]\sf{\red{︎✰}ShineBrighter\red{︎✰}}[/tex]
[tex]\sf{✍︎ C.Rose\red{❀}}[/tex]
ฅ^•ﻌ•^ฅ
if 2x + 3y = 12 and xy = 6, find the value of 8x^3 + 27y^3
Answer:
The value of [tex]8\cdot x^{3} + 27\cdot y^{3}[/tex] is 432.
Step-by-step explanation:
Let be the following system of equations:
[tex]2\cdot x + 3\cdot y = 12[/tex] (1)
[tex]x\cdot y = 6[/tex] (2)
Then, we solve both for [tex]x[/tex] and [tex]y[/tex]:
From (1):
[tex]2\cdot x + 3\cdot y = 12[/tex]
[tex]2\cdot x = 12- 3\cdot y[/tex]
[tex]x = 6 - \frac{3}{2}\cdot y[/tex]
(1) in (2):
[tex]\left(6-\frac{3}{2}\cdot y \right)\cdot y = 6[/tex]
[tex]6\cdot y-\frac{3}{2}\cdot y^{2} = 6[/tex]
[tex]\frac{3}{2}\cdot y^{2}-6\cdot y + 6 = 0[/tex]
The roots of the polynomial are determined by the Quadratic Formula:
[tex]y_{1} = y_{2} = 2[/tex]
By (1):
[tex]x = 6 - \frac{3}{2}\cdot (2)[/tex]
[tex]x = 3[/tex]
If we know that [tex]x = 3[/tex] and [tex]y = 2[/tex], then the final value is:
[tex]z = 8\cdot x^{3}+27\cdot y^{3}[/tex]
[tex]z = 8\cdot 3^{3}+27\cdot 2^{3}[/tex]
[tex]z = 432[/tex]
The value of [tex]8\cdot x^{3} + 27\cdot y^{3}[/tex] is 432.
What is the area of the yellow region?
Answer:
195 sq cm
Step-by-step explanation:
15 x 15 = 225
----------------------
3(8) + 2(3) = 30
----------------------
225 - 30 = 195 sq cm
In a 45-45-90 right triangle, what is the ratio of the length of one leg to the length of the other leg? O A. sqrt2:1 O B. 1:1 Oc. C. 2:1 O D. 1:sqrt2
Answer:
B. 1 : 1
Step-by-step explanation:
the triangle has the same size of legs (the same angles 45°)
Grade 10 Math. Solve for y. Will mark right answer brainliest :)
Answer:
y=5, y=[tex]\frac{38}{11}[/tex]
Step-by-step explanation:
Hi there!
We are given the equation
[tex]\frac{y+2}{y-3}[/tex]+[tex]\frac{y-1}{y-4}[/tex]=[tex]\frac{15}{2}[/tex] and we need to solve for y
first, we need to find the domain, which is which is the set of values that y CANNOT be, as the denominator of the fractions cannot be 0
which means that y-3≠0, or y≠3, and y-4≠0, or y≠4
[tex]\frac{y+2}{y-3}[/tex] and [tex]\frac{y-1}{y-4}[/tex] are algebraic fractions, meaning that they are fractions (notice the fraction bar), but BOTH the numerator and denominator have algebraic expressions
Nonetheless, they are still fractions, and we need to add them.
To add fractions, we need to find a common denominator
One of the easiest ways to find a common denominator is to multiply the denominators of the fractions together
Let's do that here;
on [tex]\frac{y+2}{y-3}[/tex], multiply the numerator and denominator by y-4
[tex]\frac{(y+2)(y-4)}{(y-3)(y-4)}[/tex]; simplify by multiplying the binomials together using FOIL to get:
[tex]\frac{y^{2}-2y-8}{y^{2}-7y+12}[/tex]
Now on [tex]\frac{y-1}{y-4}[/tex], multiply the numerator and denominator by y-3
[tex]\frac{(y-1)(y-3)}{(y-4)(y-3)}[/tex]; simplify by multiplying the binomials together using FOIL to get:
[tex]\frac{y^{2}-4y+3}{y^{2}-7y+12}[/tex]
now add [tex]\frac{y^{2}-2y-8}{y^{2}-7y+12}[/tex] and [tex]\frac{y^{2}-4y+3}{y^{2}-7y+12}[/tex] together
Remember: since they have the same denominator, we add the numerators together
[tex]\frac{y^{2}-2y-8+y^{2}-4y+3}{y^{2}-7y+12}[/tex]
simplify by combining like terms
the result is:
[tex]\frac{2y^{2}-6y-5}{y^{2}-7y+12}[/tex]
remember, that's set equal to [tex]\frac{15}{2}[/tex]
here is our equation now:
[tex]\frac{2y^{2}-6y-5}{y^{2}-7y+12}[/tex]=[tex]\frac{15}{2}[/tex]
it is a proportion, so you may cross multiply
2(2y²-6y-5)=15(y²-7y+12)
do the distributive property
4y²-12y-10=15y²-105y+180
subtract 4y² from both sides
-12y-10=11y²-105y+180
add 12 y to both sides
-10=11y²-93y+180
add 10 to both sides
11y²-93y+190=0
now we have a quadratic equation
Let's solve this using the quadratic formula
Recall that the quadratic formula is y=(-b±√(b²-4ac))/2a, where a, b, and c are the coefficients of the numbers in a quadratic equation
in this case,
a=11
b=-93
c=190
substitute into the formula
y=(93±√(8649-4(11*190))/2*11
simplify the part under the radical
y=(93±√289)/22
take the square root of 289
y=(93±17)/22
split into 2 separate equations:
y=[tex]\frac{93+17}{22}[/tex]
y=[tex]\frac{110}{22}[/tex]
y=5
and:
y=[tex]\frac{93-17}{22}[/tex]
y=[tex]\frac{76}{22}[/tex]
y=[tex]\frac{38}{11}[/tex]
Both numbers work in this case (remember: the domain is y≠3, y≠4)
So the answer is:
y=5, y=[tex]\frac{38}{11}[/tex]
Hope this helps! :)
Why is making a record of withdrawals and deposits in your checkbook register a good practice?
Answer:
it helps you balance your checkbook
Step-by-step explanation:
Balancing your checkbook means that you do a check in your account that shows how much money is available.
I hope it helps❤️
factorize this equation . ײ-ײy²+×y
Answer:
x(x-x[tex]y^{2}[/tex]+y)
Step-by-step explanation:
Need help on this question asap pleasee
Answer:
B
Step-by-step explanation:
9 divided by 4, then multiply by 12
Answer:
y = 2.25(12)
Step-by-step explanation:
$9 for 4 pizzas
$9/4 = $2.25
$9 for 4 pizzas is the same ratio as $2.25 per 1 pizza
To deliver x number of pizzas, the charge, y, is
y = 2.25x
For 12 pizzas, the delivery charge is
y = 2.25(12)
Help please will be marked as brainliest if correct.
Answer:
5
Step-by-step explanation:
Greater than 0
Less than 100
Is not 4, but is greater than four
Is less than 5.5
Must be a whole number
5 is the only whole number between 4 and 5.5
add 8/9 + 7/9 Simplify the answer and write as a mixed number.
Answer:
[tex]1\frac{6}{9}[/tex]
Step-by-step explanation:
[tex]\frac{8}{9}+\frac{7}{9}[/tex]
[tex]\frac{8+7}{9}=\frac{15}{9}=1\frac{6}{9}[/tex]
HELPPP ASAPPP PLAESE HELPP
Answer:
first question answer is step 2 and second step is answer step 3, last one is step is answer step 1
Which multiplication equation is false?
A) (-a)*(-1)=(-a)
B) (-a)*0=0
C) (-a)*1=(-a)
D) (-a)*b=b*(-a)
Answer:
A is wrong
Step-by-step explanation:
Answer:
A(-a)*(-1)=(-a)
Step-by-step explanation:
Anything multiplied by 0 is 0. Therefore, option B is correct.
Option A is wrong because when multiplying two negatives you should get a positive not a negative.
Anything multiplied by 0 is 0. Therefore, option B is correct
Option C is correct because a negative times a positive gives a positive.
Option D is correct because you can't solve for different times being multiplied you can only combine like terms therefore your answer will equal the same result here.
the bag of skittles has 3 parts red skittles , 5 parts yellow skittles and 7 parts orange skittle. Represent this ratio three ways;visually, using ratio notation and using fraction notation
Step-by-step explanation:
Given that,
The bag of skittles has 3 parts red skittles, 5 parts yellow skittles and 7 parts orange skittle.
Ratio notation is= 3:5:7
Frction notation,
Red skittle[tex]=\dfrac{3}{3+5+7}=\dfrac{1}{5}[/tex]
Yellow skittle [tex]=\dfrac{5}{3+5+7}=\dfrac{1}{3}[/tex]
Orange skittle [tex]=\frac{7}{3+5+7}=\dfrac{7}{15}[/tex]
Hence, this is the required solution.
What are the mensure of 1 angle and 2 angle? Show ur work or explain
Answer:
angle 1 = 105º
angle 2 = 75º
Step-by-step explanation:
angle 2 = 75º
corresponding angle to the 75º angle
angle 1 = 105º
it's supplementary to angle 2
180 - 75 = 105
Use the following number line to determine if the expressions are true or false.
Answer:
[tex]{ \tt{a < b→true}} \\ { \bf{reason :because \: - 1 \: is \: less \: than \: 4.5 }}\\ \\ { \tt{ |a| > b →false}} \\ { \bf{reason :1 \: is \: not \: greater \: than \: 4.5 }}\\ \\ { \tt{a < |b| →true}}[/tex]
Answer:
true
false
true
Step-by-step explanation:
Round to 3 SF
0.0692494
rounding 0.0692494 to 3SF is 0.069
The spinner depicted is a fair spinner. The spinner is least likely to land on which number?
A 1
B 2
C 3
D It is impossible to tell.
Answer:
d
Step-by-step explanation:
it is impossible to tell since no numbers were given nor signs were offered to help us know whether we are dealing with additon , subtraction , multiplication or division
Answer pleaseeeeee !!!
Answer:
B. Leg-Acute (LA)
E. Angle-Angle-Side (AAS)
Step-by-step explanation:
Congruence is the relationship between two or more shapes with respect to their common properties.
Comparing the properties of triangles LMN and OPQ, it would be observed that two angles are similar and one side.
So that the congruence theorems or postulates required are:
B. Leg-Acute (LA)
E. Angle-Angle-Side (AAS)
Determine whether the triangles are congruent. Explain your reasoning .
SAS (Side, Angle, Side) or ASA (Angle, Side, Angle)
Answer:
Step-by-step explanation:
First use the fact that the sum of interior angles of a triangle is 180° to find the measure of the missing angle
in ΔDEF we have 180 -68 -81 = 31°
in ΔABC we have 180 -68 -33 = 79°
the measure of the angles in ΔABC and ΔDEF are different 33°, 68°, 79° ≠81°, 68°, 31°so the two triangles are not congruent.
Question 9 Multiple Choice Worth 1 points)
(01.06 MC)
Solve the following equation for x: 2x + 5y = 8.
Answer:
x = 4 - 5/2 y
Step-by-step explanation:
2x + 5y = 8.
Subtract 5x from each side
2x + 5y -5y = 8-5y
2x = 8 -5y
Divide each side by 2
2x/2 = (8-5y)/2
x = 4 - 5/2 y
Answer:
x=[tex]\frac{-5y}{2}[/tex]+4
Step-by-step explanation:
Hi there!
We're given the equation 2x+5y=8 and we want to solve it for x
as we don't know the value of y, x won't actually be a number (it'll be an expression instead). However, we will solve this as if it was a regular equation by isolating x onto one side
here's the given equation
2x+5y=8
start by subtracting 5y from both sides
2x=-5y+8
divide both sides by 2
x=[tex]\frac{-5y}{2}[/tex]+4
Hope this helps!
What percent is represented by the shaded area?
Answer:91%
Step-by-step explanation:
Six oranges in a bag of 30 oranges are bad. Express the number of bad oranges as a fraction in its lowest terms
Answer:
1
5
is the answer
Step-by-step explanation:
hope it helps you!
I'LL MARK FIRST CORRECT ANSWER BRAINLIEST !!!
Faith makes greeting cards with colored paper. She plans to make 15 of the cards out of red paper. She has 25 sheets of colored paper in all. If she uses all the colored paper she has, how many sheets are a color other than red?
a. 5
b. 20
d. 25
c. 125
ps: any incorrect, irrelevant, plagiarized, or absurd, will be reported! sorry for the inconvenience !
Name the marked angle in 2 different ways.
Answer:
∠XWV ∠UWV
Hope this helps! :)
PLEASE HELP WILL MARK BRAINLIEST - An airplane travels 150 miles horizontally during a decrease of 35,000 feet vertically.
1. What is the angle of descent?
2. How long is the plane's path?
Answer:
[tex]\text{1. }2.53^{\circ},\\\text{2. }792,772.98\:\mathrm{ft}[/tex]
Step-by-step explanation:
Start by converting miles to feet:
[tex]150\text{ miles}=150\cdot 5280\text{ feet}=792000\text{ feet}[/tex]
Form a right triangle with the plane's displacement marking the hypotenuse of this triangle. We can now use basic trig for a right triangle to solve for the angle of descent.
Let the angle of descent be [tex]\theta[/tex]. In a right triangle, the tangent of an angle is equal to its opposite side divide by its adjacent side.
Therefore, we have:
[tex]\tan \theta=\frac{35000}{792000},\\\\\theta =\arctan(\frac{35000}{792000})=2.53036411\approx \boxed{2.53^{\circ}}[/tex]
In all right triangles, [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle (Pythagorean Theorem).
Therefore, the length of the plane's path is:
[tex]35,000^2+792,000^2=c^2,\\c^2=628489000000,\\c=\sqrt{628489000000}=792772.981376\approx \boxed{792,772.98\:\mathrm{ft}}[/tex]